Question: Simplify the following expression: $k = \dfrac{30r^2 + 10qr}{10qr + 5r} - \dfrac{20r^2 + 5r}{10qr + 5r}$ You can assume $p,q,r \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{30r^2 + 10qr - (20r^2 + 5r)}{10qr + 5r}$ $k = \dfrac{10r^2 + 10qr - 5r}{10qr + 5r}$ The numerator and denominator have a common factor of $5r$, so we can simplify $k = \dfrac{2r + 2q - 1}{2q + 1}$